A mosquito net positioned over a 7 ft × 4 ft bed has a height of 3...

Let the corner of the bed where the mosquito enters be the origin $(0, 0, 0)$.

The dimensions of the mosquito net are length $l = 7 \text{ ft}$, width $w = 4 \text{ ft}$, and height $h = 3 \text{ ft}$.

The coordinates of the diagonally opposite upper corner of the net are $(7, 4, 3)$.

The displacement vector of the mosquito from the origin to this corner is $\vec{s} = 7\hat{i} + 4\hat{j} + 3\hat{k}$.

The magnitude of the displacement is given by $|\vec{s}| = \sqrt{7^2 + 4^2 + 3^2}$.

$|\vec{s}| = \sqrt{49 + 16 + 9} = \sqrt{74} \text{ ft}$.